Asynchronous Stabilization of Nonlinear Markov Jump Singularly Perturbed Systems via Fuzzy Static Output Feedback Control

Baogang Ding,Xiaoxin Feng,Tingting Ma,Yueying Wang,Haiping Du

doi:10.1155/2021/9918054

Abstract

This study focuses on the static output feedback control of nonlinear Markov jump singularly perturbed systems within the framework of Takagi–Sugeno fuzzy approximation. From a practical point of view, the phenomenon of asynchronous switching between the plant and the controller is considered and characterized by a finite piecewise-homogenous Markov process. Particularly, for facilitating the controller synthesis, the closed-loop system is transformed into a fuzzy Markov jump singularly perturbed descriptor system by adopting descriptor representation. In order to fully accommodate the system features, an appropriate stochastic Lyapunov function is constructed. Afterwards, by combining Finsler’s lemma, the mean square exponential admissibility of the system is analyzed. The conditions ensuring the existence of the predesigned controller are given and further solved by designing a brief search algorithm. Finally, a typical circuit system is used to demonstrate the application potential of the developed control technology and the effectiveness of the control strategy.

Highlights

Analysis and synthesis of singularly perturbed systems (SPSs) have attracted significant research attention since many practical dynamical systems including the well-known power systems and nuclear reactor systems can be referred to these kind of systems [1]
There has been a growing research attention on nonlinear SPSs by Takagi–Sugeno fuzzy approximation approach, which establish an intimate connection between the fuzzy-logic technique and the perturbation analysis approach for linear SPSs [3,4,5,6]
Complexity on static output feedback controller (SOFC) design, when it comes to SPSs, the available results are scattered due to the additional complexity induced by singular perturbation structure. e recent progress is achieved in [15], where two SOFC design methods were developed for fuzzy SPSs. e first method imposes a condition that all the output matrices share the same specified matrix, which may be, hard to be fulfilled in some practical applications

Summary

Introduction

Analysis and synthesis of singularly perturbed systems (SPSs) have attracted significant research attention since many practical dynamical systems including the well-known power systems and nuclear reactor systems can be referred to these kind of systems [1]. E recent progress is achieved in [15], where two SOFC design methods were developed for fuzzy SPSs. e first method imposes a condition that all the output matrices share the same specified matrix, which may be, hard to be fulfilled in some practical applications To solve this problem, another method based on matrix transformation is further provided. (1) To circumvent the restrictive condition employed on output matrices and facilitate the controller design, the descriptor representation is adopted to transform the closed-loop system into a fuzzy Markov jump singularly perturbed descriptor system (MJSPDS) For such a complicated system, how to fully exploit the mixed system features and achieve SOFC synthesis is a challenging task.

Problem Statement

Admissibility Analysis

Simulation Study